Deep vs. Diverse Architectures for Classification Problems

This study compares various superlearner and deep learning architectures (machine-learning-based and neural-network-based) for classification problems across several simulated and industrial datasets to assess performance and computational efficiency, as both methods have nice theoretical convergence properties. Superlearner formulations outperform other methods at small to moderate sample sizes (500-2500) on nonlinear and mixed linear/nonlinear predictor relationship datasets, while deep neural networks perform well on linear predictor relationship datasets of all sizes. This suggests faster convergence of the superlearner compared to deep neural network architectures on many messy classification problems for real-world data. Superlearners also yield interpretable models, allowing users to examine important signals in the data; in addition, they offer flexible formulation, where users can retain good performance with low-computational-cost base algorithms. K-nearest-neighbor (KNN) regression demonstrates improvements using the superlearner framework, as well; KNN superlearners consistently outperform deep architectures and KNN regression, suggesting that superlearners may be better able to capture local and global geometric features through utilizing a variety of algorithms to probe the data space.Comment: Paper done as part of R&D project at Kaplan University, submitted to GCAI 201

Locality preserving projection on SPD matrix Lie group: algorithm and analysis

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For high-dimensional SPD matrices, directly using manifold learning algorithms to reduce the dimension of matrix-form data is impossible. The SPD matrix must first be transformed into a long vector, and then the dimension of this vector must be reduced. However, this approach breaks the spatial structure of the SPD matrix space. To overcome this limitation, we propose a new dimension reduction algorithm on SPD matrix space to transform high-dimensional SPD matrices into low-dimensional SPD matrices. Our work is based on the fact that the set of all SPD matrices with the same size has a Lie group structure, and we aim to transform the manifold learning to the SPD matrix Lie group. We use the basic idea of the manifold learning algorithm called locality preserving projection (LPP) to construct the corresponding Laplacian matrix on the SPD matrix Lie group. Thus, we call our approach Lie-LPP to emphasize its Lie group character. We present a detailed algorithm analysis and show through experiments that Lie-LPP achieves effective results on human action recognition and human face recognition.Comment: 15 pages, 3 table